A dual characterization of the C^1 harmonic capacity and applications

TL;DR

This paper provides a dual characterization of the C^1 harmonic capacity in high-dimensional spaces, linking it to classical capacities through the Garabedian function, with potential applications in analysis.

Contribution

It introduces a novel dual characterization of the C^1 harmonic capacity using the Garabedian function, extending classical capacity concepts.

Findings

Dual characterization of K_c via Garabedian function

Connections between high-dimensional harmonic capacities and classical capacities

Potential applications in harmonic analysis and capacity theory

Abstract

The Lipschitz and C^1 harmonic capacities K and K_c in R^n can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities G and A (respectively). In this paper we provide a dual characterization of K_c in the spirit of the classical one for the capacity A by means of the Garabedian function.